On estimating P(X > Y) for the exponential distribution

Abstract

Let X and Y be independent exponentially distributed random variables having parameters λ and μ respectively. Sharp boundsfor the first two moments of the maximum likelihood estimator and minimum variance unbiased estimator of P(X > Y) are obtained, when μ is known, say 1. When μ is unknown, sharp bounds for the first two moments of the maximum likelihood estimator of p(X > Y) are obtained and a lower bound for the variance of the minimum variance unbiased estimator is also obtained.